描述逻辑εLU概念及术语公理集的表达能力刻画  

Characterizing the Expressive Power for Concept Descriptions and Terminological Axioms Boxes in the Description Logic εLU

作　　者：申宇铭[1] 王驹[2,3] 唐素勤[2] 

机构地区：[1]广东外语外贸大学思科信息学院,广东广州510420 [2]广西师范大学计算机科学与信息工程学院,广西桂林541004 [3]高可信软件技术教育部重点实验室(北京大学),北京100871

出　　处：《软件学报》2014年第8期1794-1805,共12页Journal of Software

基　　金：国家自然科学基金(60573010;61103169);高可信软件技术教育部重点实验室开放课题(HCST201302);广西自然科学基金(2011GXNSFA018159)

摘　　要：表达能力和推理复杂性是一个逻辑的两个重要特征,也是一对相互制约的关系.解释之间的互模拟关系是从语义的角度刻画逻辑表达能力的一个有效途径,其代表性的结果是命题模态逻辑表达能力的刻画定理——van Benthem刻画定理.给出了描述逻辑εLU(含构造子:原子概念、顶概念、概念交、概念并、完全存在约束)的模拟关系,建立了εLU中概念和术语公理集的表达能力刻画定理,即一阶逻辑公式与εLU中概念和术语公理集等价的充分必要条件.上述结果为寻求表达能力与推理复杂性之间的最佳平衡提供了有效的支持.The two most important properties of a logic are its expressive power and the complexity of reasoning, which are also an opposing relation in the logic. Bisimulations between interpretations are effective way to characterize the expressive power, and the van Benthem characterization theorem is a classical result which gives an exact condition for when a first-order formula with one free variable is equivalent to a modal logic formula. This paper provides a simulation forELU （including atomic concept, top concept, conjunction concept, disjunction concept, and existential quantification）. Based on the simulation, the characterization theorems of expressive power for concept descriptions and TBoxes are established to give the sufficient and necessary conditions for when a first-order formula is equivalent to a concept description or a TBox are set up. The above results provide effective supports for the tradeoff between the expressive power and the complexity of reasoning problems.

关 键 词：描述逻辑 概念描述 术语公理集 表达能力 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]